-2y2-9=-9y-y2

Solution for -2y2-9=-9y-y2 equation:

-2y^2-9=-9y-y2

We move all terms to the left:

-2y^2-9-(-9y-y2)=0

We add all the numbers together, and all the variables

-2y^2-(-9y-1y^2)-9=0

We get rid of parentheses

-2y^2+1y^2+9y-9=0

We add all the numbers together, and all the variables

-1y^2+9y-9=0

a = -1; b = 9; c = -9;
Δ = b2-4ac
Δ = 92-4·(-1)·(-9)
Δ = 45
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{5}}{2*-1}=\frac{-9-3\sqrt{5}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{5}}{2*-1}=\frac{-9+3\sqrt{5}}{-2}
$